Quantum mechanics dominates various effects in modern research from miniaturizing electronics, up to potentially ruling solid-state physics, quantum chemistry and biology. To study these effects experimental quantum systems may provide the only effective access. Seminal progress has been achieved in a variety of physical platforms, highlighted by recent applications. Atomic ions are known for their unique controllability and are identical by nature, as evidenced, e.g., by performing among the most precise atomic clocks and providing the basis for one-dimensional simulators. However, controllable, scalable systems of more than one dimension are required to address problems of interest and to reach beyond classical numerics with its powerful approximative methods. Here we show, tunable, coherent couplings and interference in a two-dimensional ion microtrap array, completing the toolbox for a reconfigurable quantum simulator. Previously, couplings and entangling interactions between sites in one-dimensional traps have been realized, while coupling remained elusive in microtrap approaches. Our architecture is based on well isolatable ions as identical quantum entities hovering above scalable CMOS chips. In contrast to other multi-dimensional approaches, it allows individual control in arbitrary, even non-periodic, lattice structures. Embedded control structures can exploit the long-range Coulomb interaction to configure synthetic, fully connected many-body systems to address multi-dimensional problems.
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